Let’s solve this problem step-by-step:

Step 1: Find the slope of line $AB$

• The coordinates of $A$ are $(-1, -4)$ and $B$ are $(2, 5)$.
• The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of $A$ and $B$: $m_{AB} = \frac{5 - (-4)}{2 - (-1)} = \frac{5 + 4}{2 + 1} = \frac{9}{3} = 3$ So, the slope of $AB$ is 3.

Step 2: Find the slope of line $CD$

• The coordinates of $C$ are $(3, -7)$ and $D$ are $(5, -1)$.
• Using the same slope formula: $m_{CD} = \frac{-1 - (-7)}{5 - 3} = \frac{-1 + 7}{5 - 3} = \frac{6}{2} = 3$ So, the slope of $CD$ is also 3.

Step 3: Compare the slopes

Since both slopes are equal ($m_{AB} = m_{CD} = 3$), the two lines are parallel.

Final Answer:

1. The slopes of the two lines are the same.
2. The slope of $AB$ is 3.

Would you like more details on parallel lines or any other related concepts?

Here are 5 related questions to deepen your understanding:

1. How do you determine whether two lines are perpendicular?
2. What is the equation of the line passing through two given points?
3. Can two non-vertical lines with different slopes ever be parallel?
4. How do you find the slope of a vertical line?
5. How is the concept of slope used in real-life applications?

Tip: When two lines have the same slope, they will never intersect unless they are the same line, meaning they are parallel!